I AM SORRY GUYS THIS IS PRETTY LONG QUESTION, BUT ANYONE KNOWS THE BETTER METHOD TO COME TO THE SOLUTION. IF I TRY THIS PROBLEM DOING IN EXAM, WILL TAKE MY 45 MIN IN QUESTION. 🙁
A company currently has 1,000 shares of common stock outstanding with zero debt. It has the choice of raising an
additional $100,000 by issuing 9% longterm
debt or issuing 500 shares of common stock. The company has a 40%
tax rate. What level of earnings before interest and taxes (EBIT) would result in the same earnings per share (EPS)
for the two financing options?
A. An EBIT of $27,000 would result in EPS of $10.80 for both.
Incorrect B. An EBIT of $27,000 would result in EPS of $7.20 for both.
C. An EBIT of $
18,000 would result in EPS of $(7.20) for both.
D. An EBIT of $
10,800 would result in EPS of $(7.92) for both.
You answered B. The correct answer is A.
Management has the choice to obtain financing through either debt or equity. Debt will have taxdeductible
interest
associated with it, whereas the sale of additional stock will not result in any taxdeductible
item since dividends are
not considered to be a deductible expense.
The raising of funds through taking on additional debt will result in a lower EAT (earnings after taxes) due to the
$9,000 of interest expense ($100,000 × 0.09); however, the number of shares will remain at 1,000.
The raising of funds through selling additional common stock will result in a higher EAT since there will be no interest
expense; however, since there will be more outstanding shares, the net income will be divided into smaller “pieces of
the pie” in relationship to the stockholders.
EPS calculation for use of debt financing:
EPS = (EBIT Interest
((
EBIT Interest)
× 0.40)) ÷ Number of shares
EPS = (EBIT $
9,000 ((
EBIT $
9,000) × 0.40)) ÷ 1,000 shares
EPS calculation for sales of additional common shares:
EPS = (EBIT (
EBIT × 0.40)) ÷ Number of shares
EPS = (EBIT (
EBIT × 0.40)) ÷ 1,500 shares
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The solution for when EPS is equal under each of these financing options can be determined by setting the two
above equations equal to each other and solving for EBIT:
(EBIT $
9,000 ((
EBIT $
9,000) × 0.40)) ÷ 1,000 shares = (EBIT (
EBIT × 0.40)) ÷ 1,500 shares
1,500 EBIT $
13,500,000 (
600 EBIT + $5,400,000) = 1,000 EBIT 400
EBIT
300 EBIT = $8,100,000
EBIT = $27,000
Proof:
Additional Debt Additional Stock
EBIT
$27,000 $27,000
Interest 9,000 0
EBT
$18,000 $27,000
Tax 7,200 10,800
$
10,800 $16,200
======= =======
Additional debt:
EPS = Net income ÷ Number of shares outstanding
EPS = $10,800 ÷ 1,000 shares = $10.80 per share
Additional stock:
EPS = Net income ÷ Number of shares outstanding
EPS = $16,200 ÷ 1,500 shares = $10.80 per share
.